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Floor and Ceiling Functions

Floor functions map a real number x to the largest integer less than or equal to x. You can probably guess what the ceiling function does.

Trailing Number of Zeroes

         

How many trailing zeros does \(19!\) have?

Find the number of trailing zeros in \(19!\times59!\times158!.\)

If \(x!\) has \(112\) trailing zeros, what is the smallest possible integer \(x?\)

How many trailing zeros does \(247!\) have?

Find the number of trailing zeros in \(303!+304!+305!.\)

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